These days, the FMS calculates a flight plan to be followed which reaches the particular points of the flight plan at precise times, in the most effective manner possible and, for example, in the most economic manner possible. The flight plan to be followed is calculated so as to observe a required time of arrival at a constraint point (that is to say, so that the aircraft reaches the constraint point at the required time of arrival), this time being commonly referred to by the acronym RTA standing for “Required Time at Arrival”.
Currently, the FMS of an aircraft regularly checks whether the aircraft is following the flight plan to be followed. When, at a current position on the lateral trajectory, the aircraft departs from the flight plan to be followed (that is to say, departs from the predetermined tolerances in the vertical flight plan or in the speed profile relative to the respective trajectories in these plans), the FMS calculates a new flight plan, called rallying flight plan, that is assumed to have to be followed by the aircraft that has left the flight plan to be followed, rallying the flight plan to be followed. The rallying flight plan includes an estimated lateral trajectory, an estimated vertical trajectory and an estimated speed profile. To rally the flight plan to be followed, it is understood that the estimated vertical trajectory, the estimated lateral trajectory and the estimated speed profile respectively converge with the vertical and lateral trajectories to be followed and the speed profile of the flight plan to be followed until they are rallied. The rallying flight plan is calculated by prediction based on a current position of the aircraft. When the aircraft is assumed to follow a predetermined lateral trajectory, the rallying flight plan includes an estimated speed profile, an estimated vertical trajectory and the lateral trajectory. The speed profile to be followed is the horizontal component of the speed to be followed. When the estimated speed profile rejoins the speed profile to be followed, it is therefore the horizontal component of the estimated speed that converges with the speed profile to be followed. In aeronautics, the quantities used to define the speed profile are the CAS (Calibrated Air Speed, corresponding to the speed indicated on the onboard instruments) and the MACH (corresponding to the Mach number). The “horizontal speed component to be followed” (hereinafter called “speed profile to be followed”) therefore corresponds to one of these quantities. The term “horizontal speed” will hereinafter be used to mean the component of the speed of the aeroplane in the horizontal plane, expressed in the units of these CAS or MACH quantities. The rallying flight plan is obtained by integrating the state vector of the aircraft, from a current position P of the aircraft, along the future lateral trajectory (in other words with constant lateral trajectory) according to a rallying guidance setpoint.
A prediction calculation performed to rally the flight plan to be followed corresponds to integrating the state of the aircraft (according to equation 1 below) on the basis of a guidance setpoint, called rallying guidance setpoint, adapted so that the aircraft rallies with the flight plan to be followed. In practice, the state X of the aeroplane is conventionally linked to the guidance setpoint U by the following equation:dX/dt=f(X,U)  (1)in which dX/dt is the derivative of the state of the aircraft relative to time.
The state of the aircraft is a vector conventionally including the following coordinates: the position of the aircraft in the horizontal plane, its altitude, its ground speed (or speed of the aircraft relative to the ground), its vertical speed, the air speed (or speed in the air mass), the fuel, time). The ground speed is equal to the air speed to which the wind is added (the whole as a vector, projected onto the horizontal plane). The speed of the aircraft is the vector consisting of the vertical speed and the ground speed of the aircraft, as a vector.
FIGS. 1a and respectively 1b show, on a descent and approach phase between a departure point PD and an arrival point PA situated at a distance da from the departure point, examples of curves of variation of the altitude and respectively of the horizontal speed of an aircraft according to the distance traveled over the lateral trajectory. The curves represented as solid lines in FIGS. 1a and 1b respectively, show the vertical trajectory to be followed PH and the speed profile to be followed PV. The curves represented as dotted lines in FIGS. 1a and 1b respectively represent an estimated vertical trajectory PHE and, respectively, an estimated speed profile PVE. In FIGS. 1a and 1b, it will be observed that, at the current point P situated at a distance dP from the start of the descent phase on the lateral trajectory, the aircraft has a current horizontal speed V and current altitude H. In FIG. 1a, the current altitude is greater than the altitude h defined by the vertical trajectory to be followed PH at the current point. The altitude difference DH is greater, as an absolute value, than a predetermined altitude tolerance TH that is not represented.
The state of the aircraft is integrated according to the rallying guidance setpoint including, between the current point P and a rejoining point at horizontal speed RV situated at a distance dv from the departure point, a rejoining guidance setpoint. More particularly, between the current point P and a first point P1 situated at a distance d1 from the departure point, a rejoining guidance setpoint of the idle thrust acceleration type is chosen such that the FPA slope (not represented) formed between the aircraft and the ground, is greater than that which is defined by the vertical trajectory to be followed in order to enable the aircraft to converge with the vertical trajectory to be followed. Between the current point and the point P1, the estimated horizontal speed of the aircraft increases (and is greater than the horizontal speed of the speed profile to be followed). Once the estimated vertical trajectory is sufficiently close to the vertical trajectory to be followed, in this at the point P1, the FMS integrates the state of the aircraft according to a rejoining guidance setpoint of the idling type, in order for the estimated vertical trajectory to rejoin the trajectory to be followed (at the altitude rejoining point RH situated at a distance dh from the departure point) and the estimated speed rejoins the speed to be followed (at the speed rejoining point RV). For a conventional aircraft in which the vector U of guidance setpoints includes two components, namely the trim of the aeroplane (or FPA slope) and the thrust of the engines, it is possible to use the trim to accelerate (increase the thrust) or slow down (reduce the trim).
As soon as the estimated vertical speed and the estimated vertical trajectory have rejoined the speed profile to be followed and, respectively, the vertical trajectory to be followed, that is to say, between the speed rejoining point RV and the arrival point PA situated at a distance da from the departure point, the FMS integrates the state of the aircraft along the flight plan to be followed. Everything takes place as if the FMS were integrating the state of the aircraft according to a guidance profile called following guidance setpoint adapted so that the estimated speed profile and the estimated vertical trajectory are equal, to within the respective tolerances, to the speed profile to be followed and to the vertical trajectory to be followed. In other words, after the respective rallying points, the estimated profiles and trajectories respectively follow the profiles and trajectories to be followed. The rallying guidance setpoint therefore includes a rejoining guidance setpoint followed by a following guidance setpoint.
The FMS calculates the estimated time of arrival at the constraint point, namely the time at which the FMS predicts that the aircraft will arrive at the constraint point. The estimated time of arrival is commonly designated by the acronym ETA (Estimated Time of Arrival). It is conventionally calculated by integrating the state vector X of the aircraft according to the rallying guidance setpoint on the future lateral trajectory. If the estimated time of arrival departs from a predetermined tolerance, called absolute tolerance T, relative to the required time of arrival RTA, a new calculation cycle takes place, causing the FMS to redefine the flight plan to be followed by taking account of the time constraint to be observed and a rallying flight plan when the aircraft departs from the flight plan to be followed. The aim is to have the estimated time of arrival calculated from the guidance setpoint converge with the required time of arrival. The tolerance with respect to the required time of arrival is generally modelled in the form of a funnel, which means that it becomes narrower as the aircraft approaches the constraint point. For the calculation of the rallying flight plan in the case where the aircraft is following a predetermined lateral trajectory, the FMS has only two degrees of freedom, namely thrust and trim, to define the rallying guidance setpoints in order to rally with the flight plan to be followed. Thus, the guidance setpoint acts on the speed of the aircraft.
The time of passage at a determined point (or time profile) is a consequence of the speed profile, so each time the aircraft leaves the vertical trajectory to be followed, the guidance setpoint determined by the guidance module acting on the horizontal speed of the aircraft causes the keeping to the time constraint to fail. A divergent infinite loop then takes place in the previously described iteration process generally resulting in failure to comply with the time constraint, but also possibly having a negative impact on the observance of the altitude and speed profiles to be followed.
Operationally, the pilot observes that, immediately after the calculation of a flight plan to be followed, the aircraft observes the time constraint but that, after the determination of a guidance setpoint bringing the aircraft to the flight plan to be followed, the aeroplane starts to deviate in time from the time constraint. After a certain time, the estimated time of arrival differs from the required time of arrival and a new calculation of the speed profile and of the vertical trajectory to be followed takes place to try to observe this time constraint, resulting in the calculation of a new guidance setpoint, different from the preceding one. From the guidance point of view, this results in hops, engine jolts if the guidance setpoints for rejoining change from one loop to another. Since the aeroplane guidance does not succeed in being stabilized on a guidance setpoint which observes the constraint, the flight management system is not reliable. The crew has a tendency to finish its manoeuvre manually. Moreover, the changes of guidance setpoint are uncomfortable for the passengers. The instability of the status of the time constraint (which changes from the “success” state to the “fail” state in each iteration) is also counter-productive with regard to the air traffic control authorities which are generally the source of the time constraint. The authorities observe that the aeroplane is no longer observing a time constraint and may therefore take a decision that is pointless, or even counter-productive, to manage the guidance of the aircraft.